Rudolf Mathar

Optimum positioning of base stations for cellular radio networks

Finding optimum base station locations for a cellular radio network is considered as a mathematical optimization problem. Dependent on the channel assignment policy, the minimization of interferences or the number of blocked channels, respectively, may be more favourable. In this paper, a variety of according analytical optimization problems are introduced. Each is formalized as an integer linear program, and in most cases optimum solutions can be given. Whenever by the complexity of the problem an exact solution is out of reach, simulated annealing is used as an approximate optimization technique. The performance of the different approaches is compared by extensive numerical tests.

Location tracking of mobiles in cellular radio networks

Some useful services in cellular radio networks and also a class of handover algorithms require knowledge of the present position and velocity of mobiles. This paper deals with a method to track mobiles by on-line monitoring of field strength data of surrounding base stations at successive time points. Such data is available in present global system for mobile communication (GSM) systems each 0.48 s and also in code-division multiple-access (CDMA) systems for transmission control. Because of strong random fluctuations of the signals, appropriate smoothing is the key point of the procedure. We develop a locally linear prediction model of successive positions as a basis for Kalman filtering. This approach turns out to be extremely successful, achieving average mislocations of 70 m in simulated test runs. Further improvement is possible by using external geographical information.

Estimating position and velocity of mobiles in a cellular radio network

Determining the position and velocity of mobiles is an important issue for hierarchical cellular networks since the efficient allocation of mobiles to large or microcells depends on its present velocity. We suggest a method of tracing a mobile by evaluating subsequent signal-strength measurements to different base stations. The required data are available in the Global System for Mobile (GSM) system. The basic idea resembles multidimensional scaling (MDS), a well-recognized method in statistical data analysis. Furthermore, the raw data are smoothed by a linear regression setup that simultaneously yields an elegant, smoothed estimator of the mobiles speed. The method is extensively tested for data generated by the simulation tool GOOSE.

Channel assignment in cellular radio networks

The authors investigate algorithms based on simulated annealing to solve the channel assignment problem for cellular radio networks. The blocking probability of a network is chosen as the optimization criterion. In order to check the quality of the solutions obtained by simulated annealing, they examine some special types of networks which allow an effective calculation of optimal solutions by tailored algorithms. Their investigations show that simulated annealing is a very powerful tool for solving channel assignment problems. >

Power control, capacity, and duality of uplink and downlink in cellular CDMA systems

Accurate power control is an essential requirement in the design of cellular code-division multiple-access (CDMA) systems. In this paper, we contribute three main themes to the power control problem. First, we derive an efficient algorithm for computing minimal power levels for large-scale networks within seconds. Nice and intuitive conditions for the existence of feasible power solutions follow from this approach. Second, we define the capacity region of a network by the set of effective spreading gains, or data rates, respectively, which can be supplied by the network. This is achieved by bounding the spectral radius of a certain matrix containing system parameters and mutual transmission gain information. It is shown that the capacity region is a convex set. Finally, we reveal an interesting duality between the uplink and downlink capacity region. In a clear-cut analytical way, it substantiates the fact that the uplink is the more restricting factor in cellular radio networks. The same methods carry over to certain models of soft handover. In the case that the channel gains are subject to log-normal shadowing, we introduce the concept of level-/spl alpha/ capacity regions. Despite the complicated structure, it can still be shown that this set is sandwiched by two convex sets coming arbitrarily close as variance decreases.

Dynamic cell association for downlink sum rate maximization in multi-cell heterogeneous networks

In this work, we consider a heterogeneous network consisting in several macro nodes and pico nodes. Our goal is to associate users, belonging to this network, to one of the nodes, while maximizing the sum rate of all users. We also want to analyze the load balancing achieved by this association. Therefore, we develop a new theoretical framework to study cell association for the downlink of multi-cell networks and derive an upper bound on the achievable sum rate. We propose a dynamic cell association heuristic, which achieves performance close to optimal. Finally, we verify our results through numerical evaluations and implement the proposed heuristic in an LTE simulator to demonstrate its viability.

On the distribution of cumulated interference power in Rayleigh fading channels

This paper deals with the distribution of cumulated instantaneous interference power in a Rayleigh fading channel for an infinite number of interfering stations, where each station transmits with a certain probability, independently of all others. If all distances are known, a necessary and sufficient condition is given for the corresponding distribution to be nondefective. Explicit formulae of density and distribution functions are obtained in the interesting special case that interfering stations are located on a linear grid. Moreover, the Laplace transform of cumulated power is investigated when the positions of stations follow a one- or two-dimensional Poisson process. It turns out that the corresponding distribution is defective for the two-dimensional models.

Pulse-coupled decentral synchronization

Synchronous firing of biological oscillators is explained by a mathematical model developed by Mirollo and Strogatz [SIAM J. Appl. Math., 50 (1990), pp. 1645–1662]. Exactly the same principles may be carried over to achieve decentral synchronization in time-division multiple access systems. However, some extensions of the basic model are necessary in view of technical implementations. This paper deals with synchronization in finite time for two oscillators and convergence to synchrony except on a set of initial conditions of measure zero for cliques of oscillators, particularly for nondifferentiable (e.g., piecewise linear) state functions. Moreover, for oscillator pairs we prove synchronization even if there is a certain delay between transmission and reception of pulses. A simulation tool, named ImDeSy, is developed to investigate general networks of oscillators with arbitrary topologies and more refined reaction strategies. This is demonstrated in two extensive examples.

The majorization approach to multidimensional scaling for Minkowski distances

The majorization method for multidimensional scaling with Kruskals STRESS has been limited to Euclidean distances only. Here we extend the majorization algorithm to deal with Minkowski distances with 1≤p≤2 and suggest an algorithm that is partially based on majorization forp outside this range. We give some convergence proofs and extend the zero distance theorem of De Leeuw (1984) to Minkowski distances withp>1.

Designing an ASIP for Cryptographic Pairings over Barreto-Naehrig Curves

This paper presents a design-space exploration of an application-specific instruction-set processor (ASIP) for the computation of various cryptographic pairings over Barreto-Naehrig curves (BN curves). Cryptographic pairings are based on elliptic curves over finite fields--in the case of BN curves a field